$\"\"$

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The function $\"\"$ is continuous for all real numbers.

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Need to varify $\"\"$ .

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Consider $\"\"$ .

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Let $\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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Apply limits: $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .